Flexible ceramic waveguides for terahertz applications and use as on-board interconnects

ABSTRACT

A terahertz (THz) waveguide and method for production allows for THz waveguides to be used in or on a printed circuit board (PCB) such that the propagation of THz waves require less power, result in less signal loss due to radiation or dispersion, and propagate more efficiently. Additionally, the position and/or geometry of a waveguide, as well as any additional antenna or coupling element, may be adjusted on or in the PCB such that the electromagnetic field of the waveguide may more efficiently couple with the electromagnetic field of the PCB.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority under 35 U. S. C. § 119of U.S. Provisional Application Ser. No. 62/895,200 filed on Sep. 3,2019 the contents of which are relied upon and incorporated herein byreference in their entirety as if fully set forth below.

BACKGROUND

Optical communication systems typically operate at the near-infraredbands of the electromagnetic spectrum having wavelengths on the order of800 nm to 2000 nm. Other types of communication systems such as cellphone systems operate at radio-wave band of the electromagnetic (EM)spectrum from about 3 KHz to 60 GHz, with plans to extend this rangeinto the microwave and millimeter bands, which extend up to about 300GHz. The move to higher and higher RF and microwave frequencies has beenenabled in part by developments in state of the art complementarymetal-oxide-semiconductor (“CMOS”)-based EM radiation sources andreceivers that can operate at frequencies greater than 100 GHz.

The terahertz wavelength range of the EM spectrum is generallyconsidered to range from 0.1 THz (=100 GHz) to 10 THz (10,000 GHz),where the corresponding free-space wavelength is denoted λ0 and is inthe range from 3 mm to 0.03 mm. In a dielectric material with the realpart of the dielectric constant ε′, the wavelength λ is given byλ=λ0/(ε′)^(1/2). More generally, the dielectric constant is expressed asε=ε′+iε″ where ε″, is the imaginary or lossy part of the dielectricconstant. Terahertz (“THz”) waveguides can be formed from a guidingstructure in which the real part of the dielectric constant is higherthan that of the surrounding material or space. Such waveguides can beused to confine and transport a THz optical signal from a sourcelocation to a receiver location.

The sub-mm wave or THz band (i.e., having a wavelength between 0.1 mm-1mm) is one of the least explored sections of the electromagneticspectrum. This is due to the historical cost of sources and detectorsand a lack of a low-loss guiding structures, equivalent to an opticalfiber that may be used with visible and infrared wavelengths.Traditional microstrip line circuits, or metallic waveguides atmicrowave frequencies are generally insufficient to support low loss THzband propagation because high-frequency signals may be absorbed by thematerials. Similarly dielectric waveguide for millimeter waves havegenerally been lossy due to radiation and/or subject to dispersion andhave been difficult to costly to use. Even the modern surface plasmonpolariton waveguides are too lossy for long-distance transmission in THzbands. Lossy means having or involving the dissipation of electrical orelectromagnetic energy.

Most THz waveguides are made of a metal or a plastic and are not made ofceramic materials. While fused silica glass has relatively goodtransmission at THz frequencies, it is relatively fragile as compared tometal and plastic and therefore makes it difficult to form acommercially viable THz waveguide product. Said differently, acommercially viable THz waveguide product needs to have bothsufficiently low loss in the THz frequency range and be mechanicallyrobust so that it can be handled for manufacturing and operate forextended periods of time in a wide range of environments.

Yeh et al. has proposed a concept for overcoming this drawback anddescribes a new family of an ultra-low-loss rectangular single-modewaveguide structure for propagating THz signals, which has anattenuation constant more than 100× less than that of a conventionaldielectric or metallic waveguide. Cavour Yeh et al., Low-Loss TerahertzRibbon Waveguides, 44 APPLIED OPTICS 28, 5937 (2005); Cavour Yeh et al.,Communication at Millimetre-Submillimetre Wavelengths Using a CeramicRibbon, 404 NATURE 584 (2000). The material Yeh et al. uses is a highpurity alumina “rectangular rod” (99.8% purity, 10:1 aspect ratio with0.635 mm in thickness, 6.35 mm in width and 910 mm in length), operatedin 30-40 GHz. However, the thickness of the rectangular rod limits itsapplication in higher frequency signals and its flexibility.

For high speed interconnects, optical transceivers can be co-packagedwith an integrated package carrying basic components and commonfunctionalities for a programmable logic circuit (“PL IC”) or anapplication-specific integrated circuit customized for a particular use(“ASIC”) on the same substrate to reduce the length of electricalinterconnects to a few millimeters for 112 GB/s and above electricalsignal links. The reduced length between electrical interconnects isrequired because of high loss of electrical signals at higherfrequencies and an increase in power consumption. Power and costs can besaved when transceivers are close to the integrated circuit (“IC”) andoptically interconnected with the fiber network of the building (e.g.datacenter) or between buildings. Today, fiber array units (FAU) are afiber assembly with an array of fibers aligned in a V-groove andend-face polished. The FAU is actively aligned to electronic integratedcircuits (PIC) and permanently attached to provide a connector interfaceto the transceiver. The fiber length can be short for pluggabletransceivers or customized in length for other applications.

In some aspects, waveguides may be used as a transmission line to guideelectromagnetic waves. For example, waveguides may confineelectromagnetic waves to propagate in one dimension such that the waveslose a reduced amount of power as it propagates during transmission.Waveguides may be configured for the transmission of electromagneticwaves at different wavelengths. For example, waveguides may beconfigured to transmit electromagnetic wavelengths within the visible,infrared, radio, microwave, or terahertz bands of the electromagneticspectrum though the useful range of operation of a particular waveguidetechnology is typically limited. Waveguides may be designed to minimizeloss (e.g., dissipation of energy) while maintaining flexibility,specific dimensions, shape, or the other properties for the desired enduse. In some examples, waveguides configured to guide electromagneticwaves within a certain band of the electromagnetic spectrum may bedifferent than waveguides configured to guide electromagnetic waveswithin a different band of the electromagnetic spectrum. In this way,waveguides may be designed (e.g., shape, dimensions, material, or thelike) to optimize performance based on the wavelengths of theelectromagnetic spectrum the waveguide is intended to transmit.

Applicant's cutting-edge technology, continuous firing process, andribbon ceramics products offers the manufacturing of an ultra-highpurity alumina ribbon waveguide with an extremely thin form factor andlong length. The attributes of Applicant's waveguides provide for anideal solution for THz communication and could address the drawbacksmentioned above. These attributes include, but are not limited to, anultrahigh purity alumina that enables great dielectric performance, afine grain size that provides for excellent flexibility and mechanicalstrength, a thin form factor, and a long length. Applicants havedeveloped a new way to cost effectively fabricate an attractive materialinto a form factor that is beneficial for the microwave/mmWaveapplications and configurations to make use of such a material.

SUMMARY

The present disclosure relates to the use of ceramic dielectricwaveguides resulting in the low loss propagation of high-frequencysignals in or on printed circuit boards. One aspect of the presentdisclosure is an assembly, comprising: a printed circuit board (PCB)assembly comprising opposite first and second ends and at least one PCBlayer wherein the at least one PCB layer comprises at least oneconductive element, an integrated circuit (IC) operably disposed on thetop surface of the PCB assembly by I/O pads, the IC having at least oneIC device, a at least one coupling element, a ceramic dielectricterahertz (THz) waveguide for guiding signals having a THz frequency inthe range from about 0.1 THz to about 10 THz comprising a ceramic corecomprising an alumina ribbon wherein the alumina ribbon has a dielectricconstant (Dk1) and a cladding surrounding the ceramic core, wherein thecladding has a dielectric constant (Dk2) such that Dk2<Dk1, and a majorsurface and an access aperture wherein the major surface is disposedbetween the first end and second end, and the ceramic dielectricwaveguide is mounted to the top surface of at least one PCB layer, theceramic dielectric terahertz (THz) waveguide comprising a first-endsection with an end face accessible through the access aperture. Inanother aspect, the printed circuit board is an optical-electricalprinted circuit board (OE-PCB).

In another aspect, the ceramic core is surrounded on two parallel sidesby at least one cutout. In a further aspect, the at least one cutout isempty. In an alternative aspect, the at least one cutout is filled witha dielectric material having a dielectric constant lower than thedielectric constant that of the ceramic core. In a further aspect, thedielectric material is polymer, glass, or silicon dioxide. In yet afurther aspect, the polymer is selected from the group consisting ofpolytetrafluoroethylene (PTFE), SU-8, fluoropolymers, and polystyrene,polyimide (Kapton or Cirlex), parylene-N, high-density polyethylene(HDPE), polypropylene (PP) and polyethylene cyclic olefin copolymer(Topas), polybenzoxazole (PBO), benzocylobutene (BCB), and liquidcrystal polymers.

In another aspect, the at least one cutout has a bending angle of atleast 10 degrees, alternatively at least 20 degrees, alternatively atleast 30 degrees, alternatively at least 40 degrees, alternatively atleast 45 degrees, alternatively at least 50 degrees, alternatively atleast 60 degrees, alternatively at least 70 degrees, alternatively atleast 80 degrees, or alternatively at least 90 degrees. In anotheraspect, the at least one cutout progressively tapers along thepropagation direction. In yet another aspect, the cutout comprises anarray of holes. In a further aspect, the array of holes creates anelectronic bandgap cladding layer. In a further aspect, the holes areuniform in shape, size, and/or linear placement. In yet a furtheraspect, the holes vary in size along the propagation direction.

In another aspect, the electronic assembly further comprises a cavityfor a source component and a cavity for a detector component on oppositeterminal ends of the ceramic dielectric terahertz (THz) waveguide. Inanother aspect, the source component is a transmitter or transceiver. Inyet another aspect, the detector component is a receiver or receive sideof a transceiver. Transceiver it is device with a transmitter andreceiver and is used in most bidirectional communication applications.

In another aspect, the electronic assembly further comprises a strut,wherein the strut consists of an alumina ribbon, and wherein the strutis at the terminal ends of the ceramic dielectric terahertz (THz)waveguide. In another aspect, the electronic assembly further comprisesa least one strut, wherein the strut is transverse to the ceramicdielectric terahertz (THz) waveguide.

In another aspect, the ceramic dielectric terahertz (THz) waveguide isfully or partially embedded within the printed circuit board (PCB)assembly. In yet another aspect, the ceramic dielectric terahertz (THz)waveguide is disposed between at least two PCB layers. In yet anotheraspect, the ceramic dielectric terahertz (THz) waveguide is mounteddirectly on the top surface of the printed circuit board (PCB) assembly.

In another aspect, the coupling element is located on the top, thebottom, or the first or the second end of the printed circuit board(PCB) assembly. In yet another aspect, the coupling element acts as anantenna. A coupling element can be used to launch the signal from aconducting/metallic waveguide into the dielectric waveguide. Such acoupling element may be referred to as an ‘antenna’, but a human orcomputer designed/optimized coupling element does not need to look likea conventional antenna.

In another aspect, at least one end of the ceramic dielectric terahertz(THz) waveguide is tapered. In a further aspect, the coupling elementruns along the tapered edge to the top surface of the printed circuitboard (PCB) assembly. In another aspect, the coupling element isconnected directly to at least one PCB layer. In another aspect, thecoupling element is connected to at least one PCB layer through at leastone conductive via. In yet another aspect, the coupling element couplesa conductive transmission waveguide to a dielectric waveguide.

In another aspect, the electronic assembly further comprises a glasssubstrate mounted on the top surface of the printed circuit board (PCB)assembly. In yet another aspect, the ceramic dielectric terahertz (THz)waveguide is mounted on the top surface of the glass substrate.

In another aspect, the electronic assembly further comprises aport/interface component. In a further aspect, the port/interfacecomponent is mounted on each source and detector component.

In another aspect, the ceramic core has a circular, elliptical orrectangular cross-sectional shape. In another aspect, the ceramicdielectric terahertz (THz) waveguide is non-planar. In yet anotheraspect, the ceramic dielectric terahertz (THz) waveguide is planar andthe ceramic core has opposite first and second planar surfaces and athickness in the range from 10 μm to 500 μm; and the cladding is definedby first and second planar layers respectively disposed immediatelyadjacent the first and second planar surfaces of the ceramic core, thefirst and second layers having dielectric constants (Dk2 and Dk3) suchthat Dk2<Dk1 and Dk3<Dk1.

One aspect of the present disclosure is a ceramic dielectric terahertz(THz) waveguide for guiding signals having a THz frequency in the rangefrom about 0.1 THz to about 10 THz comprising a ceramic core comprisingan alumina ribbon wherein the alumina ribbon has a dielectric constant(Dk1), wherein the ceramic core is surrounded on at least two parallelsides by at least one cutout, wherein the at least one cutout create anelectronic bandgap cladding layer, and wherein the electronic bandgapcladding layer has a dielectric constant (Dk2) such that Dk2<DK1.

In another aspect, the at least one cutout is empty. In an alternativeaspect, the at least one cutout is filled with a dielectric materialhaving a dielectric constant lower than the dielectric constant that ofthe ceramic core. In a further aspect, the dielectric material ispolymer, glass, or silicon dioxide. In yet a further aspect, the polymeris selected from the group consisting of polytetrafluoroethylene (PTFE),SU-8, fluoropolymers, and polystyrene, polyimide (Kapton or Cirlex),parylene-N, high-density polyethylene (HDPE), polypropylene (PP) andpolyethylene cyclic olefin copolymer (Topas), polybenzoxazole (PBO),benzocylobutene (BCB), and liquid crystal polymers.

In another aspect, the at least one cutout has a bending angle of atleast 10 degrees, alternatively at least 20 degrees, alternatively atleast 30 degrees, alternatively at least 40 degrees, alternatively atleast 45 degrees, alternatively at least 50 degrees, alternatively atleast 60 degrees, alternatively at least 70 degrees, alternatively atleast 80 degrees, or alternatively at least 90 degrees. In anotheraspect, the at least one cutout progressively tapers along thepropagation direction. In an alternative aspect, the at least one cutoutcomprises an array of holes. In a further aspect, the holes are uniformin shape, size, and/or linear placement. In a further alternativeaspect, the holes vary in size along the propagation direction.

The presently described and claimed technology has numerous advantages,including, but not limited to, (1) reducing manufacturing costs forparallel links in a circuit; (2) simplifying alignment of a transmitteror receiver by precisely creating patterns in a sheet of ceramicmaterial due to its rigid structure; (3) saving power within the circuitdue to no longer needing to convert from electrical to optical signalsor optical to electrical signals; (4) simplifying transmitter and/orreceiver assembly; (5) having lower loss than conventional conductivewaveguides at mm wave frequencies because mm waves can be exciteddirectly in dielectric THz waveguides without costly and high-losslasers and photodetectors; (6) industrializing known waveguidefabrication techniques that provide high quality waveguides, e.g., laserhole formation or singulation, dielectric dip-coating or coating die;(7) more easily creating interconnects through the use of waveguidesembedded as a sheet of ceramic material; (8) using effective indexcladding material allowing for fine tuning of the confinement of theguided electromagnetic radiation and the number of propagating modes;(9) creating transitions in that confinement that can more easily bemade in effective index material, such as soot by localized heating andsintering of the silica particles along the propagation direction; and(10) creating THz waveguides with different rigid geometries makingcoupling more efficient. providing a millimeter wave waveguidingtechnology that can be readily incorporated into established electroniccircuit board fabrication and assembly techniques

These and other advantages and novel features of the present invention,as well as details of illustrated aspects thereof will be more fullyunderstood from the following description and from the figures.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

These as well as other features of the present invention will becomemore apparent upon reference to the drawings wherein:

FIG. 1 illustrates a cross-section view of multiple alumina waveguidessurrounded by a dielectric material embedded within a printed circuitboard.

FIG. 2 illustrates a cross-section view of multiple alumina waveguidesdirectly on a common dielectric substrate all surrounded by a differentdielectric material embedded within a printed circuit board.

FIG. 3 illustrates a cross-section view of a wire bond link between atransmitter and receiver mounted directly on top of a printed circuitboard wherein the ribbon is made of alumina and may be encapsulated by adielectric material or air.

FIG. 4 illustrates a cross-section view of a sample configuration of anelectronic circuit board assembly and a waveguide coupling elementembedded within the printed circuit board (PCB) assembly to couple theelectrical transmission signal to the mounted ceramic dielectricterahertz (THz) waveguide.

FIG. 5 illustrates a cross-section view of a sample configuration ofassembly and multiple coupling elements embedded within the printedcircuit board (PCB) assembly to couple the electrical transmissionsignal to the embedded ceramic dielectric terahertz (THz) waveguide.

FIG. 6 illustrates a cross-section view of a sample configuration of aassembly with a ceramic dielectric terahertz (THz) waveguide tapered onone end and mounted on the printed circuit board (PCB) assembly and aconductive element running along the tapered end to a conductive pathway(“via”) where the via intersects with PCB layers embedded within theprinted circuit board (PCB).

FIG. 7 illustrates a cross-section view of a sample configuration of aassembly with a ceramic dielectric terahertz (THz) waveguide tapered onone end and mounted on a printed circuit board (PCB) assembly and acoupling element running along the tapered end to a PCB layer within theelectronic assembly.

FIG. 8 illustrates a cross-section view of a sample configuration of anassembly with a mounted dielectric material encompassing a glasssubstrate used to support a ceramic dielectric terahertz (THz) waveguideand a coupling element which connects to a via where the via intersectswith a PCB layer embedded within the printed circuit board (PCB)assembly

FIG. 9A illustrates a top view of alumina ribbon cut out in regions tocreate straight pathways that run along the x-axis. FIG. 9B illustratesa top view of alumina ribbon cut out in regions to create a 90 degreewaveguide bend.

FIG. 10A illustrates a top view of alumina ribbon cut out in regions tocreate an adiabatic taper for mode conversion. FIG. 10B illustrates atop view of alumina ribbon cut out in regions to create asplitter/combiner.

FIG. 11A illustrates a top view of alumina ribbon wherein a ceramicdielectric terahertz (THz) waveguide is terminated by cutouts. FIG. 11Billustrates a top view of alumina ribbon with periodic cross braceswherein a waveguide is terminated.

FIG. 12 illustrates a side view of a multi-layer stack of waveguides.

FIG. 13A illustrates a ceramic dielectric terahertz (THz) waveguide withan array of hole creating a uniform electronic bandgap cladding layer.FIG. 13B illustrates a ceramic dielectric terahertz (THz) waveguide withan array of hole creating a tapered electronic bandgap cladding layer.

The foregoing summary, as well as the following detailed description ofcertain features of the present application, will be better understoodwhen read in conjunction with the appended drawings. For the purposes ofillustration, certain features are shown in the drawings. It should beunderstood, however, that the claims are not limited to the arrangementsshown in the attached drawings.

DETAILED DESCRIPTION

Referring generally to the figures, aspects of the present disclosurerelate to the use of a ceramic dielectric waveguide to couple anelectrical transmission line signal with that of a printed circuitboard. Advantageously, the shape and position of the ceramic dielectricwaveguide with respect to the printed circuit board adjusts how theelectromagnetic field of the waveguide couples with that of theconductive structures within the printed circuit board, creatingopportunities to make propagation of THz waves more efficient and lesslossy. Also advantageously, the potential addition coupling elementssuch as antenna elements creates more opportunities for the same. Somepotential shapes and positions of the ceramic dielectric waveguide,along with the potential addition of antenna or coupling elements, willbe discussed in the following sections. The aspects described herein arefor the purposes of illustration and should not be considered limiting.

Waveguide Creation

The present disclosure relates to waveguides configured to transmitelectromagnetic waves within the THz range that include a ceramic coreand an optional dielectric material cladding. Amongst other factors,propagation of an electromagnetic wave is influenced by the size andshape of the waveguide. In some aspects, a ceramic core with smallercross-sectional dimensions may be more suitable for transmitting wavesin the THz range than a core with larger cross-sectional dimensions. Theceramic core may have a cross-sectional dimension in the range of about10 microns to about 500 microns (μm), preferably about 20 μm. The crosssectional dimension is not limited to rectangular cross-sectional shapesbut may be applied interchangeably to circular, elliptical, or othercross-sectional shapes.

The ceramic core may be comprised of any suitable ceramic material andmay be rectangular or ribbon-shaped. Electromagnetic waves propagatewithin the confines of the walls of a waveguide, with the walls actingas boundaries. Therefore, some cross-sectional shapes may be moresuitable for transmitting waves in the THz range than othercross-sectional shapes.

In some aspects, the THz waveguide may have a long form factor. In theseaspect, the THz waveguide 10 may have a length 12 of about 3 centimeters(cm) or greater. A longer form factor may be more suitable fortransmitting waves in the THz range than a shorter form factor.Similarly, a longer form factor may be more suitable for transmittingwaves over a longer distance than a shorter form factor that transmitswaves over a shorter distance.

In other aspects, the THz waveguide may also be thin. For example, itmay have a rectangular cross-section of a THz waveguide having a widthand a height. In this aspect, the ceramic core may have a width orheight in the range of about 20 μm to about 500 μm, preferably about 20μm. A ceramic core with a smaller width and/or height may be moresuitable for transmitting waves in the THz range than a ceramic corewith a larger width and/or height. Similarly, a ceramic core with asmaller width and/or height may be more suitable for THz applicationsrequiring smaller waveguides, e.g. inter-chip interconnects orchip-to-chip communication.

In some aspects, the THz waveguides may transmit signals in thefrequency range of about 0.1 THz to about 10 THz with a ceramic corecomprised of alumina. In other aspects, an alumina core may be comprisedof ultra-high purity alumina with a purity level of about 99% or higher,about 99.5% or higher, about 99.75% or higher, about 99.9%, about 99.95%or higher, about 99.96% or higher, or about 99.99% or higher. In yet afurther aspect, the alumina has a purity of about 99.96% or higher. Inthese aspects, an alumina core with a high purity level enables greaterdielectric performance than an alumina core with lower purity level. Inone aspect, the core may have a Dk in the range of 10-1000 and adissipation factor (“Df”) in the range of less than 1×10⁻³, preferably aDk=10 and a Df<=1×10⁻⁴, respectively. In view of the present aspects, awaveguide comprised of a high purity alumina core can effectivelytransmit signals within the THz range while still having lowtransmission loss.

In other aspects, the alumina ceramic core may have a Dk of ε_(r),surrounded by air. A high dielectric constant can enable single modeoperation in a wide frequency window. Waveguide propagation modes dependon the operating wavelength and polarization, along with the shape andsize of the waveguide. For the rectangular waveguide shown in FIG. 1A,normalized frequency parameters are provided below:

$V_{x} = {\frac{2\pi\; f}{c}w\sqrt{ɛ_{r} - 1}}$$V_{y} = {\frac{2\pi\; f}{c}h\sqrt{ɛ_{r} - 1}}$

For single mode operation in both the x and y directions, V_(x)=π, andV_(y)=π. The cutoff frequency for single mode operation can bedetermined by the following equations:

$f_{c} = {\frac{C}{2w\sqrt{ɛ_{r} - 1}}\mspace{14mu}{for}\mspace{14mu}{single}\mspace{14mu}{mode}\mspace{14mu}{in}\mspace{14mu}{the}\mspace{14mu} x\text{-}{direction}}$$f_{c} = {\frac{C}{2h\sqrt{ɛ_{r} - 1}}\mspace{14mu}{for}\mspace{14mu}{single}\mspace{14mu}{mode}\mspace{14mu}{in}\mspace{14mu}{the}\mspace{14mu} y\text{-}{direction}}$

Depending on the form factor of the waveguide and its dielectricproperties, a waveguide can permit single mode operation at a highcut-off frequency. Single mode operation can be achieved if thewaveguide dimensions width (w) and height (h) satisfy the aboveequations. For material with a high dielectric constant, the waveguidedimensions can be reduced for single mode operation. Small waveguidedimensions increase the waveguide density for waveguide arrays used ininterconnects and improve the mechanical flexibility. For a suitablydimensioned alumina ceramic ribbon waveguide having low-loss and a highdielectric constant, the waveguide can exhibit an attenuationcoefficient of less than 10 dB/cm.

A THz waveguide needs to have both low transmission loss in the THzfrequency and a wide range of mechanical properties that allow foroperation in a variety of environmental conditions. In one aspect, theceramic core comprises alumina and may have a grain size of at leastabout 0.5 μm. A ceramic core that comprises alumina with a smaller grainsize can be denser and may exhibit more flexibility than a ceramic corewith a larger grain size. In some aspects, ceramic core that comprisesalumina with a grain size of at least about 0.5 μm may have variableflexibility, e.g. a bending radius of about 17 mm for a form factor witha thickness in the range from about 10 μm to about 200 μm. In view ofthe present aspects, a waveguide comprised of a ceramic core thatcomprises alumina can effectively transmit signals within the THz rangewhile still having low transmission loss and improved flexibility.

Conventional waveguides that exhibit flexibility may still fracture orshatter when exposed to a variety environmental conditions. Therefore, aTHz waveguide that has greater mechanical strength but remains flexible,pliable, or supple, may be more suitable for terahertz applications. Asdiscussed above, a ceramic core that comprises alumina with a smallergrain size can be denser and may exhibit more flexibility, andmechanical strength, than a ceramic core that comprises alumina with alarger grain size. In some aspects, a ceramic core that comprisesalumina with a grain size of at least about 0.5 μm may have a mechanicalstrength of at least 700 MPa when undergoing a 2pt flexural bendingstrength test. In view of the present aspects, a waveguide comprised ofa ceramic core that comprises alumina can effectively transmit signalswithin the THz range while still having low transmission loss andimproved strength.

In other aspects, the ceramic core material is not limited to alumina;core material may also include, for example, silica (Dk˜4), mullite(Dk˜6), magnesium titinate (Dk˜15-20), zirconium tin titinate (Dk˜37),titânia (Dk˜100), or barium titinate (Dk>1000). Other core materials arecontemplated that similarly transmit signals in the frequency range of0.1 THz to 10 THz but provide for a high Dk.

In some aspects, a THz waveguide may have a cladding disposed around aceramic core that comprises alumina. A cladding serves as a protectivegliding material for a ceramic core thereby enabling propagation in theTHz range with low transmission loss. In addition, a cladding mayinhibit any potential interactions between a propagating wave and thesurrounding environment.

A cladding can be disposed around a ceramic. In some aspects, it may bepreferable for cladding to have a lower dielectric constant than thedielectric constant of core. In other aspects, it may be preferable forcladding to have a Df less than 1×10⁻³. As a result, cladding may assistin confining an electromagnetic wave inside the ceramic core structureso that it limits how much the fields spread out, and losses resultingfrom this effect are eliminated. It is advantageous for cladding to havea similar loss tangent in the THz range as the ceramic core (though itcan be somewhat higher because the total loss is less sensitive to thecladding), as well as a low dielectric constant so to minimizetransmission loss and the size of the structure formed as part of thewaveguide. In some aspects, cladding may have a dielectric constantwithin the range of 10-1000.

Cladding 25 can be made of air, glass, silicon dioxide (silica glass),or polymers. In aspects where cladding 25 is made of a polymer, polymersmay include, for example, SU-8, polytetrafluoroethylene (Teflon), orother fluoropolymers that have low loss properties in the frequencyrange of 100 GHz-1000 GHz. Other suitable materials for the cladding 18may be any combination thereof.

As discussed above, FIG. 1D shows an aspect where a THz waveguide mayhave a planar configuration. In this aspect, the ceramic core 21 may becomprised of opposite first 22 and second 23 planar surfaces. FIG. 5shows one aspect where a cladding is defined by a first 27 and second 28planar layer that may be respectively disposed immediately adjacent tothe first 29 and second 30 planar surfaces of the ceramic core.

In some aspects, it may be preferable for the first planar 27 layer ofthe cladding to have a lower dielectric constant than the dielectricconstant of ceramic core. In other aspects, it may be preferable for thesecond 28 planar layer of the cladding to have a lower dielectricconstant than the dielectric constant of the ceramic core. In otheraspects, it may be preferable for both the first 27 and second 28 planarlayers of the cladding to have lower dielectric constants than thedielectric constant of the ceramic core. As a result, the first 27 andsecond 28 planar layers of the cladding may assist in confining anelectromagnetic wave inside the ceramic core structure so that it doesnot spread out, and losses resulting from this effect are eliminated. Itis advantageous for the first and second planar layers of the claddingto have a similar loss tangent in the THz range as the ceramic core, aswell as a low Dk so to minimize transmission loss and the size of thestructure formed as part of the waveguide.

In yet another aspect, it may be preferable for the first planar 27layer of the cladding to have a Df less than 1×10⁻³. In other aspects,it may be preferable for the second 28 planar layer of the cladding tohave a Df less than 1×10⁻³. In other aspects, it may be preferable forboth the first 27 and second 28 planar layers of the cladding to have aDf less than 1×10⁻³. As a result, the first 27 and second 28 planarlayers of the cladding may assist in confining an electromagnetic waveinside the ceramic core structure so that it does not spread out, andlosses resulting from this effect are eliminated. It is advantageous forthe first and second planar layers of the cladding to have a similarloss tangent in the THz range as the core, as well as a low DF so tominimize transmission loss and the size of the structure formed as partof the waveguide.

The first and second planar layers of the cladding can be made of air,glass, silicon dioxide (silica glass), or polymers. In aspects where thefirst and second planar layers of the cladding are made of a polymer,polymers may include, for example, SU-8, polytetrafluoroethylene(Teflon), or other fluoropolymers that have low loss properties in thefrequency range of 100 GHz-1000 GHz. Other suitable materials for thecladding 18 may be glass, air, polymer and any combination thereof.

In aspects where a cladding is disposed around a ceramic core, thewaveguide may become stiff, inflexible, or fragile. In addition,disposing a cladding around a ceramic core may increase the overall sizeof the waveguide. Therefore, the thickness of a cladding may influencethe flexibility, durability, and size of a waveguide. In one aspect, thecladding comprises a thickness 31 in the range from 0.1 mm to 10 mm. Inanother aspect, the first and second planar layers of a claddingcomprises a thickness in the range of 0.1 mm to 10 mm. Because of thethickness of a cladding, a THz waveguide may remain flexible with theadded benefit of reducing the overall size of the waveguide structure.

FIG. 9A illustrates a top view of a ceramic ribbon 40 cut out in regions42 to create an array of THz waveguides 14. Each ceramic ribbon 40 mayrange from 1 mm to 100 mm in width. Each cutout 42 may range from 10 umto 5 mm in width. Each waveguide 14 may range from 100 nm to 1 mm inwidth. Each cutout 42 may be created by laser cutting, ablation,perforation and separation process, or any similar process.

A cutout 42 may be filled with air, forming a cladding layer betweeneach waveguide 14. Cladding material can be composed of two materials ofdiffering dielectric constants acting as an effective index materialsuch that they retain their distinct composition in local regions uponcombination, the size of these distinct regions being much less than theTHz operating wavelength, and on average the dielectric constant of thecladding material is lower than the dielectric constant of the THzwaveguide 14. An example of cladding material could be a fluoropolymerwhere it is made porous with air bubbles to lower the dielectricconstant and the pore size is much less than the THz operatingwavelength. Another example of cladding material could be silica sootdeposited as a cladding. Pore size as deposited is small enough thatsilica soot need not be consolidated. Localized heating andconsolidation can be done to create transitions in the THz waveguideeffective index that can be useful for mode field conversion.Alternatively, any or all cutouts 42 may also be filled with adielectric material, for example a polymer, having a lower dielectricconstant than a THz waveguide 14. Each cutout 42 shown runs in astraight line, but it is also contemplated within the scope of thepresent invention that it may contain a bend, for example a cutoutcurved by somewhere between 0-90 degrees (see FIG. 9B).

FIG. 10A illustrates a top view of a ceramic ribbon 40 cut out inregions 42 to create an adiabatic taper for THz waveguide modeconversion along the propagation direction. This allows for couplingbetween a THz waveguide with a relatively wide width to a THz waveguidewith a relatively narrow width, or vice versa depending on the directionof propagation. Each ceramic ribbon 40 may range from 1 to 100 mm inwidth. Each cutout 42 may range from 10 um to 5 mm in width. Eachwaveguide 14 may range from 100 nm to 1 mm in width before the taper andfrom 1 um to 1 mm in width after the taper. Each cutout 42 may becreated by laser cutting, ablation, perforation and separation process,or any similar process. A cutout 42 may be filled with air, forming acladding layer between waveguides 14. Alternatively, any or all cutouts42 may also be filled with a dielectric material, for example a polymer,having a lower dielectric constant than a THz waveguide 14. Rather thanan adiabatic taper, a ceramic ribbon 40 may be cut out in regions 42 tocreate a splitter or combiner, depending on the propagation direction(see FIG. 10B). The splitter shown has a waveguide 14 splitting in totwo separate waveguides 14, but it is also contemplated within the scopeof the present invention that a waveguide 14 may split in to two or moreparts. Likewise, the combiner shown has two separate waveguides 14combining into one waveguide 14, but it is within the scope of thepresent invention that a combiner may combine two or more separatewaveguides 14.

FIG. 11A illustrates a top view of a ceramic ribbon 40 cut out inregions 42 to create a THz waveguide 14. A cutout 42 exists near eachend of the waveguide 14 allowing space for a transmitter 44 and receiver46. Each cutout 42 may be created by laser cutting, ablation,perforation and separation process, or any similar process. Between theTHz waveguide 14 and the space for a transmitter 44 or receiver 46 is atleast one strut, which comprises a strip of ceramic ribbon, 48 with awidth much less than a single THz frequency wavelength. The narrow widthof the strut 48 between the THz waveguide 14 creates edge coupling ofTHz electromagnetic radiation into or out of the waveguide 14 from asource 20 or detector 22, respectively. To add more mechanical supportto the THz waveguide 14, struts 48 may be added transverse to theceramic dielectric terahertz waveguide, creating smaller cutout regions42 (see FIG. 11B).

FIG. 12 illustrates a side view of multiple layers of ceramic ribbon 40separated from each other by layers of dielectric material 50 having alower dielectric constant than the THz waveguide 14. Each layer ofceramic ribbon 42 may have embedded within it one or more THz waveguides14, one or more waveguide devices, one or more sources (e.g.,transmitters) 20, and/or one or more detectors (e.g. receivers) 22. Eachlayer of dielectric material 50 acts as a waveguide material and may bea polymer or other suitable material with a dielectric constant lowerthan that of the THz waveguide 14. The layers shown are singular (i.e.,alternating one layer of dielectric material with one layer of ceramicribbon), but it is within the scope of the present invention that theremay be one or more layers of dielectric material 50 between each layerof ceramic ribbon 40. It is also within the scope of the presentinvention that there may be one or more layers of ceramic ribbon 40between each layer of dielectric material 50.

FIG. 13A illustrates a top view of a ceramic ribbon 40 cut out in anarray of circular holes 54 uniform in shape, size, and placement in theregion adjacent to the THz waveguide 14 to create a electronic bandgapcladding layer for a THz waveguide 14. Advantageously, light cannotpropagate in a electronic bandgap, so light propagation is bound to thecore region (i.e., the THz waveguide 14). Each ceramic ribbon 40 mayrange from 1 to 100 mm in width. Each cutout 54 may range from 10 um to5 mm in diameter, and are preferably created with a laser. Eachwaveguide 14 may range from 100 nm to 1 mm in width. A cutout 54 may befilled with air, forming a electronic bandgap cladding layer for a THzwaveguide 14. Alternatively, any or all cutouts 54 may be filled with adielectric material, for example a polymer, having a lower dielectricconstant than a THz waveguide 14. The cutouts 54 in the ceramic ribbon40 provide mechanical support for the THz waveguide 14 withoutdisrupting coupling or propagation or creating excess loss. The cutouts54 shown are identical, but it is within the scope of the presentinvention that each cutout 54 may be a shape other than circular, forexample, square, rectangular, triangular, or any other polygonal ornon-polygonal shape. It is also within the scope of the presentinvention that the placement of each cutout 54 may be sporadic and notuniform in placement. It is also within the scope of the presentinvention that the size of each cutout 54 may differ. FIG. 13B, forexample, illustrates a top view of a ceramic ribbon 40 cut out in anarray of circular holes 54 moving from largest in diameter to smallestin diameter. Variation in the size of the array of holes along thepropagation direction creates a taper by varying properties of the THzfrequency wave propagating through the THz waveguide 14.

Wire Bonds

FIG. 3 illustrates a cross-section of a printed circuit board 10 havingassembled on its top surface at least one transmitter component 20 andat least one receiver component 22. Each transmitter component 20 andreceiver component 22 includes a connecting port/interface 24 where aceramic alumina wire 56 may be placed post-assembly thereby connectingthe port/interface 24 of the two components 20, 22. Post-assemblyplacement of the ceramic alumina wire 56 may enable embeddedinterconnects for surface mount assembly and interconnect of atransmitter 20 or receiver 22 to the THz waveguide 14. Advantageously,this allows flexibility in pick and place assembly of each transmitter20 and receiver 22, solder reflow, and/or adhesive bonding. The ceramicalumina wire 56 is flexible enough so that it may be coiled. If coiled,the ceramic alumina wire 56 is compact enough that it may be readilyunreeled during wire bonding. Advantageously, this allows for each wirebond to be created within seconds. Also advantageously, gold ball wirebonding processes and other state-of-the-art wire bonding tools may beused. Additionally, UV curable adhesives may be used where the ceramicalumina wire 56 is attached to a port/interface 24. UV curable adhesivehas the dielectric property of being low loss and may have a dielectricconstant lower than that of the ceramic alumina wire 56. The length ofthe ceramic alumina wire 56 may range from 10 cm to 100 m. Each ceramicalumina wire 56 may have a ceramic alumina core 14 coated in adielectric material having a dielectric constant lower than that of theceramic alumina core 14, for example a polymer or any other suitablesubstance. The dielectric material coating the ceramic alumina core 14provides a cladding layer for the ceramic alumina core 14. The ceramicalumina wire 56 may have a protective or shielding layer (e.g., ametal). After the ceramic alumina wire 56 is connected to aport/interface 24, it may be embedded in a dielectric material having alower dielectric constant than that of the ceramic alumina wire 56, forexample a polymer, air, or any other suitable material.

Planar Ceramic Dielectric Waveguide

FIG. 1 illustrates a cross-section of a printed circuit board 10 havinga ceramic dielectric waveguide 16 embedded within its circuit substrateand extending along the z-axis. The printed circuit board 10 may becomprised of one or more layers of ceramic, glass, or other suitablematerials. The ceramic dielectric waveguide 16 may be comprised of atleast one ceramic core 14, for example alumina, zirconia, titania,silica, or any other suitable material, embedded within anotherdielectric 12, for example a polymer, glass, or any other suitablematerial. The surrounding dielectric 12 becomes a cladding so that thestrip(s) of ceramic dielectric become the core for guiding THz frequencywaves. The surrounding dielectric 12 has a lower dielectric constantthan the ceramic core 14 to ensure the THz wave propagates through thewaveguide efficiently. The ceramic dielectric waveguide 16 shown has arectangular configuration, but it is also contemplated within the scopeof the present invention that it may have a configuration other thanrectangular, for example circular, elliptical, triangular, or any otherpolygonal or non-polygonal shape. The ceramic core 14 is likewise shownhaving a rectangular configuration, but it is also contemplated withinthe scope of the present invention that it may have a configurationother than rectangular, for example circular, elliptical, triangular, orany other polygonal or non-polygonal shape.

Also embedded within the ceramic dielectric waveguide 16 may be aceramic support structure 18 (see FIG. 2), where the ceramic supportstructure 18 is comprised of the same material as the ceramic core andruns perpendicular to the ceramic core 14 along the x-axis. When theceramic support structure 18 is present at least one ceramic dielectricwaveguide 14 can rest directly on top of the ceramic support structure18.

FIG. 4 illustrates a cross-section of a printed circuit board 10 havinga ceramic dielectric waveguide 16 mounted directly on the top surface ofthe circuit substrate. Along a portion of the top surface of the circuitsubstrate, below the ceramic dielectric waveguide 16, may run an antennaor coupling element 30. The antenna or coupling element 30 may couplethe electrical transmission line signal from the integrated circuit (IC)26 to the ceramic dielectric waveguide 16 containing a ceramic core 14.The IC 26 drives the electrical signal through the printed circuit board10. The IC 26 may be connected to the printed circuit board 10 by metalinput/output (I/O) pads 28 that conduct signals in and out of theintegrated circuit. The electrical signal generated by the IC 26 may bepropagated through vias 32 to PCB conductive layers 34 embedded withinthe printed circuit board 10. The same electrical signal may further bepropagated through PCB conductive layers 34 and/or more vias 32 to theantenna or coupling element 30 which may couple the signal to theceramic dielectric waveguide 16. The antenna or coupling element 30shown runs horizontally along the bottom of the ceramic dielectricwaveguide 16, but it is also contemplated within the scope of thepresent invention that it may run vertically along the end surface ofthe ceramic dielectric waveguide 16. The mixture of vertical andhorizontal coupling elements can be used to optimize the coupling toindividual modes guided within the dielectric waveguide.

FIG. 5 illustrates a cross-section of a printed circuit board 10 havinga ceramic dielectric waveguide 16 embedded within its circuit substrate.Along portions of the top and the bottom surfaces of the ceramicdielectric waveguide 16 may be antennas or coupling elements 30 whichmay act as a conductive transmission line waveguide to couple theelectrical transmission line signal from the IC 26 to the ceramicdielectric waveguide 16. The antenna or coupling elements 30 may connectto embedded conductive layers 34 within the printed circuit board 10either directly or through one or more vias 32. The antenna or couplingelements may connect to the IC 26 either directly or through embeddedconductive layers 34 and vias 32. The antenna or coupling elements 30shown run horizontally along a portion of the top and the bottomsurfaces of the ceramic dielectric waveguide 16, but it is alsocontemplated within the scope of the present invention that it may runhorizontally along a portion of only the top surface of the ceramicdielectric waveguide 16 or along a portion of only the bottom surface ofthe ceramic dielectric waveguide 16. It is also contemplated within thescope of the present invention that the antenna or coupling element 30may run vertically along the end surface of the ceramic dielectricwaveguide 16. It is also contemplated within the scope of the presentinvention that the antenna or coupling element 30 may run in acombination of these orientations, including but not limited to,horizontally along the bottom surface and vertically along the endsurface of the ceramic dielectric waveguide 16, horizontally along thetop surface and vertically along the end surface of the ceramicdielectric waveguide 16, and horizontally along the bottom and topsurfaces and vertically along the end surface of the ceramic dielectricwaveguide 16.

FIG. 6 illustrates a cross-section of a printed circuit board 10 havinga ceramic dielectric waveguide 16 mounted directly on the top surface ofthe circuit substrate. The ceramic dielectric waveguide 16 may have alinearly tapered left edge, along which may run an antenna or couplingelement 30. The taper or other transition regions increase coupling fromthe antenna or coupling element 30 which launches the signal into theceramic dielectric waveguide 16. When the ceramic dielectric waveguide16 is on the same plane as the IC 26, the antenna or coupling element 30running along the tapered edge of the ceramic dielectric waveguide 16may connect to embedded conductive layers 34 within the printed circuitboard 10 through a via 32. When the ceramic dielectric waveguide 16 ison a lower plane than the IC 26 (see FIG. 7), the antenna or couplingelement 30 running along the tapered edge of the ceramic dielectricwaveguide 16 may directly connect to embedded conductive layers 34within the printed circuit board 10. If the IC 26 is on a higher planethan the ceramic dielectric waveguide 16, the IC may still connect tothe embedded conductive layers 34 through a via 32. The ceramicdielectric waveguide 16 is shown having a linearly tapered left edgesurface, but it is also contemplated within the scope of the presentinvention that any edge may be linearly tapered. It is also contemplatedwithin the scope of the present invention that the ceramic dielectricwaveguide 16 may have an exponential taper, logarithmic taper, or anyother curved taper creating a non-vertical edge. The ceramic dielectricwaveguide 16 is shown on the same plane (see FIG. 6) or lower plane (seeFIG. 7) compared to the IC 26, but it is contemplated within the scopeof the present invention that the ceramic dielectric waveguide 16 may beon a higher plane compared to the IC 26.

FIG. 8 illustrates a cross-section of a printed circuit board 10 havinga glass substrate 36 mounted directly on the top surface of the circuitsubstrate. The glass substrate 36 may support the ceramic dielectricwaveguide 16 which rests directly on top of the glass substrate 36.Encompassing the glass substrate 36 and the ceramic dielectric waveguide16 may be a dielectric material 12, for example a polymer or any othersuitable substance with a dielectric constant lower than that of theceramic dielectric waveguide 16. The dielectric material 12 encompassingthe glass substrate 36 and ceramic dielectric waveguide 16 is shown, butit is also contemplated within the scope of the present invention thatthe dielectric material 12 is an optional element. Encompassed by theglass substrate 36 and connected to the ceramic dielectric waveguide 16may be an antenna or coupling element 30. The glass substrate 36supporting the ceramic dielectric waveguide 16 provides a low losssubstrate for the antenna or coupling element 30 to launch an electricsignal into the ceramic dielectric waveguide 16. The antenna or couplingelement 30 may be connected to a via 32 which may intersect between theglass substrate 36 and the circuit substrate of the printed circuitboard 10. The via 32 may further intersect with one or more embeddedconductive layers 34 within the printed circuit board 10.

In the present disclosure, use of the singular includes the pluralexcept where specifically indicated.

The present described technology is now described in such full, clear,concise, and exact terms as to enable any person skilled in the art towhich it pertains to practice the same. It is to be understood that theforegoing described preferred aspects of the technology and thatmodification may be made therein without departing from the spirit ofscope of the invention as set forth in the appended claims. The scope ofthe following claims is to be accorded the broadest interpretation toencompass all such modifications and equivalent structures andfunctions. Therefore, it is intended that the application not be limitedto the particular aspects disclosed, but that the application willinclude all aspects falling within the scope of the appended claims.

The invention claimed is:
 1. An electronic assembly, comprising: aprinted circuit board (PCB) assembly comprising first and second endsand at least one PCB layer wherein the at least one PCB layer comprisesat least one conductive element, an integrated circuit (IC) operablydisposed on the top surface of the PCB assembly by I/O pads, the IChaving at least one IC device, at least one coupling element; a ceramicdielectric terahertz (THz) waveguide for guiding signals having a THzfrequency in the range from about 0.1 THz to about 10 THz comprising aceramic core comprising an alumina ribbon wherein the alumina ribbon hasa dielectric constant (Dk₁) and a cladding surrounding the ceramic core,wherein the cladding has a dielectric constant (Dk₂) such that Dk₂<Dk₁,and a major surface and an access aperture wherein the major surface isdisposed between the first end and second end, and the ceramicdielectric waveguide is mounted to the top surface of at least one PCBlayer, the ceramic dielectric terahertz (THz) waveguide comprising afirst-end section with an end face accessible through the accessaperture.
 2. The electronic assembly according to claim 1, wherein thePCB comprises multiple ceramic dielectric THz waveguides.
 3. Theelectronic assembly according to claim 1, wherein the ceramic dielectricterahertz (THz) waveguide is fully or partially embedded within theprinted circuit board (PCB) assembly.
 4. The electronic assemblyaccording to claim 1, the ceramic dielectric terahertz (THz) waveguideis disposed between at least two PCB layers.
 5. The electronic assemblyaccording to claim 1, further comprising a cavity for a source ortransceiver component and a cavity for a detector or transceivercomponent on opposite terminal ends of the ceramic dielectric terahertz(THz) waveguide.
 6. The electronic assembly according to claim 5,wherein the source component is a transmitter.
 7. The electronicassembly according to claim 5, wherein the detector component is areceiver.
 8. The electronic assembly according to claim 5, furthercomprising a strut, wherein the strut consists of an alumina ribbon, andwherein a strut is at the terminal ends of the ceramic dielectricterahertz (THz) waveguide.
 9. The electronic assembly according to claim5, further comprising at least one strut, wherein the strut istransverse to the ceramic dielectric terahertz (THz) waveguide.
 10. Theelectronic assembly according to claim 1, wherein the ceramic core issurrounded on two parallel sides by at least one cutout.
 11. Theelectronic assembly according to claim 10, wherein the at least onecutout is empty.
 12. The electronic assembly according to claim 10,wherein the at least one cutout has a bending angle of at least 10degrees.
 13. The electronic assembly according to claim 10, wherein theat least one cutout progressively tapers along the propagationdirection.
 14. The electronic assembly according to claim 10, whereinthe at least one cutout is filled with a dielectric material having adielectric constant lower than the dielectric constant that of theceramic core.
 15. The electronic assembly according to claim 14, whereinthe dielectric material is polymer, glass, or silicon dioxide.
 16. Theelectronic assembly according to claim 15, wherein the polymer isselected from the group consisting of polytetrafluoroethylene (PTFE),SU-8, fluoropolymers, and polystyrene, polyimide (Kapton or Cirlex),parylene-N, high-density polyethylene (HDPE), polypropylene (PP) andpolyethylene cyclic olefin copolymer (Topas), polybenzoxazole (PBO),benzocylobutene (BCB), and liquid crystal polymers.
 17. The electronicassembly according to claim 10, wherein the at least one cutoutcomprises an array of holes.
 18. The electronic assembly according toclaim 17, wherein the array of holes creates a electronic bandgapcladding layer.
 19. The electronic assembly according to claim 17,wherein the holes are uniform in shape, size, and/or linear placement.20. The electronic assembly according to claim 17, wherein the holesvary in size along the propagation direction.